Tailored Functionally Graded Materials design and concurrent topology optimization with implicit fields

The 12th International Symposium on Multiscale, Multifunctional and Functionally Graded Materials (FGM-2012) was held in Beijing, China, from 22–36 October 2012. This was part of a series of conferences organized every two years endorsed by International Advisory Committee for FGM's, which serves as a forum for scientists, educators, engineers and young students interested in the development of functionally graded materials (FGM). The series continues from the previous international symposium on FGM held in Sendai, Japan (1990), San Francisco, USA (1992), Lausanne, Switzerland (1994), Tsukuba, Japan (1996), Dresden, Germany (1998), Estes Park, USA (2000), Beijing, China (2002), Leuven, Belgium (2004), Hawaii, USA (2006), Sendai, Japan (2008) and Guimaraes, Portugal (2010). Functionally graded materials are non-uniform materials which are designed with embodied continuous spatial variations in composition and microstructure for the specific purpose of adjusting their thermal, structural, mechanical, biological or functional response to specific application conditions. Such multi-phase materials cover a range of space and time scales, and are best understood by means of a comprehensive multiscale, multiphysics approach. These kinds of materials are presently in the forefront of materials research, receiving worldwide attention. They have a broad range of applications including for example, biomedical, biomechanical, automotive, aerospace, mechanical, civil, nuclear, and naval engineering. New applications are continuously being discovered and developed. The objective of the FGM-2012 intends to provide opportunities for exchanging ideas and discussing state-of-the-art theories, techniques and applications in the fields of multiscale, multifunctional and FGM, through invited lectures, oral and poster presentations. FGM-2012 was organized and hosted by University of Science and Technology Beijing, China, together with Tsing-hua University and Wuhan University of Technology, and was supported by National Natural Science Foundation of China. On behalf of the organizing committee of FGM-2012, I express my great appreciation to their support of the symposium. Nearly 100 scholars and students from Japan, Brazil, Germany, Russia, United States of America, Portugal, France, Switzerland, Turkey, Singapore, China, and so on, attended FGM-2012, and 57 of the presented papers were collected and selected for publication. The subjects of these papers cover simulation and characterization, advanced fabrication technology, novel application of FGM and layer materials. I cordially thank all of the authors and attendees for their support, and my appreciation is also given to the advisory committee, organizing committee, and the conference volunteers for their hard work. Professor Zhangjian Zhou Proceedings Editor Beijing, December 2012CommitteesInternational Advisory Committee Professor Glaucio H Paulino, USA Professor Marek-Jerzy Pindera, USA Professor Jeong-Ho Kim, USA Professor Emer Fazil Erdogan, USA Professor Dr Monika Willert-Porada, Germany Professor Emer Wolfgang G J Bunk, Germany Professor Omer Van Der Biest, Belgium Professor Michael M Gasik, Finland Professor Evgeny Levashov, Russia Professor Lianmeng Zhang, China Professor Qingjie Zhang, China Professor Wei Pan, China Professor Chang-Chun Ge, China Professor Jing-Feng Li, China Professor Zhangjian Zhou, China Associate Professor Serkan Dag, Turkey Professor Fernando A Rochinha, Brazil Professor Emilio C N Silva, Brazil Professor Luis August Rocha, Portugal Dr Sasa Novak, Slovenia Dr Masayuki Niino, Japan Professor Akira Kawasaki, Japan Professor Ichiro Shiota, Japan Dr Akinaga Kumakawa, Japan Dr Yoshikazu Shinohara, Japan Professor Kiyotaka Matsuura, Japan Professor Yoshinari Miyamoto, Japan Professor Takashi Goto, Japan Professor Yoshimi Watanabe, Japan Professor Kazuhiro Hasezaki, Japan Professor Soshu Kirihara, Japan Professor Emer Toshio Hirai, Japan Mr Choji Endou, Japan Dr Seiichi Uemura, Japan Local Organizing Committee Professor Changchun Ge (Chairman) Professor Xuanhui Qu Professor Jingfeng Li Professor Wei Pan Professor Lianmeng Zhang;Professor Qingjie Zhang Professor Qiang Shen Professor Jianghong Gong Dr Xianhui LiDr Min Xia

Concurrent topology optimization of sandwich structures with multi-configuration and variable-diameter lattice infill

Microstructural design of connective base cells for functionally graded materials

Tailoring specified vibration modes is a requirement for designing piezoelectric devicesaimed at dynamic-type applications. A technique for designing the shape of specifiedvibration modes is the topology optimization method (TOM) which finds an optimummaterial distribution inside a design domain to obtain a structure that vibrates accordingto specified eigenfrequencies and eigenmodes. Nevertheless, when the TOM is applied todynamic problems, the well-known grayscale or intermediate material problem arises whichcan invalidate the post-processing of the optimal result. Thus, a more natural way forsolving dynamic problems using TOM is to allow intermediate material values. This idealeads to the functionally graded material (FGM) concept. In fact, FGMs are materialswhose properties and microstructure continuously change along a specific direction.Therefore, in this paper, an approach is presented for tailoring user-defined vibrationmodes, by applying the TOM and FGM concepts to design functionally gradedpiezoelectric transducers (FGPT) and non-piezoelectric structures (functionally gradedstructures—FGS) in order to achieve maximum and/or minimum vibration amplitudes atcertain points of the structure, by simultaneously finding the topology and materialgradation function. The optimization problem is solved by using sequential linearprogramming. Two-dimensional results are presented to illustrate the method.

Reliability-based design optimization of volume fraction distribution in functionally graded composites

Background: Functionally graded material (FGM) is popularly recognized as promising material for modern engineering applications, which has gained attention of researchers due to its composition design and mechanical behaviour. FGM is the most suitable choice as a structural material for conical pressure vessel and requires detailed analysis for its mechanical behaviour. Objective: The design optimization of the rotating truncated conical shell made from FGM subjected to internal pressure (variable and constant) using Finite Element Method. Method: Using a commercially available finite element code, the effect of various parameters (such as cone angle, internal pressure, and angular velocity) on truncated conical shell was analyzed. The material properties and composition vary along the radial direction according to the exponential function. Results: Under the chosen circumstances 10¹ cone angle, 4-12MPa internal pressure, and 50 rad/sec rotational velocity were found most suitable. Conclusion: The results also demonstrated that chosen parameters (such as, cone angle, internal pressure, and rotational velocity) significantly affect the stresses working on conical shell. This requires careful selection while designing the conical pressure vessel. These optimization results are helpful for research community to design a conical shell pressure vessel using FGM.

The present work introduces a novel concurrent optimization formulation to meet the requirements of lightweight design and various constraints simultaneously. Nodal displacement of macrostructure and effective thermal conductivity of microstructure are regarded as the constraint functions, which means taking into account both the load-carrying capabilities and the thermal insulation properties. The effective properties of porous material derived from numerical homogenization are used for macrostructural analysis. Meanwhile, displacement vectors of macrostructures from original and adjoint load cases are used for sensitivity analysis of the microstructure. Design variables in the form of reciprocal functions of relative densities are introduced and used for linearization of the constraint function. The objective function of total mass is approximately expressed by the second order Taylor series expansion. Then, the proposed concurrent optimization problem is solved using a sequential quadratic programming algorithm, by splitting into a series of sub-problems in the form of the quadratic program. Finally, several numerical examples are presented to validate the effectiveness of the proposed optimization method. The various effects including initial designs, prescribed limits of nodal displacement, and effective thermal conductivity on optimized designs are also investigated. An amount of optimized macrostructures and their corresponding microstructures are achieved.

This paper presents a study on the concurrent topology optimization of a structure and its material microstructure. A modified optimization model is proposed by introducing microstructure orientation angles as a new type of design variable. The new model is based on the assumptions that a structure is made of a material with the same microstructure, and the material may have a different orientation within the design domain of the structure. The homogenization theory is applied to link the material and structure scales. An additional post-processing technique is developed for modifying the obtained design to avoid local optima caused by the use of orientation angle variables. Numerical examples are presented to illustrate the viability and effectiveness of the proposed model. It is found that significant improvement in structural performance can be achieved by optimizing the orientation of microstructures in concurrent topology optimization of structures and materials. This paper presents a modified concurrent optimization model with three kinds of design variables. At the micro scale, topological design variables are employed for describing the distribution of base material within a material cell so that the material microstructure can be defined. At the macro scale, in addition to topological design variables for describing the distribution of material with microstructure within the design domain, microstructure orientation angles are introduced for defining material axis directions at different locations. Numerical examples have shown that significant improvement in the performance of optimized designs can be achieved.

One of the properties of composite materials is the possibility of having phononic band gaps, within which sound and vibrations at certain frequencies do not propagate. These materials are called Phononic Crystals (PCs). PCs with large band gaps are of great interest for many applications, such as transducers, elastic/ acoustic filters, noise control, and vibration shields. Most of previous works concentrates on PCs made of elastic isotropic materials; however, band gaps can be enlarged by using non-isotropic materials, such as piezoelectric materials. Since the main property of PCs is the presence of band gaps, one possible way to design structures which have a desired band gap is through Topology Optimization Method (TOM). TOM is a computational technique that determines the layout of a material such that a prescribed objective is maximized. Functionally Graded Materials (FGM) are composite materials whose properties vary gradually and continuously along a specific direction within the domain of the material. One of the advantages of applying the FGM concept to TOM is that it is not necessary a discrete 0-1 result, once the material gradation is part of the solution. Therefore, the interpretation step becomes easier and the dispersion diagram obtained from the optimization is not significantly modified. In this work, the main objective is to optimize the position and width of piezocomposite materials band gaps. Finite element analysis is implemented with Bloch-Floquet theory to solve the dynamic behavior of two-dimensional functionally graded unit cells. The results demonstrate that phononic band gaps can be designed by using this methodology.

Topology optimization for concurrent design of layer-wise graded lattice materials and structures

Multiscale concurrent topology optimization of transient thermoelastic structures

Concurrent topology optimization of macrostructures and material microstructures for natural frequency

This paper studies two-scale concurrent topology optimization with multiple micro heterogeneous materials subject to volume constraints. Unlike the existing work on concurrent two-scale optimization where only one material with optimal microstructure is used or that with multiple micro material where each material is distributed in a number of prescribed geometrical domains, selection of micro heterogeneous materials in this work is based on direction of principal stresses in macro structure. For a structure composed of m micro materials, the macro elements are classified into m categories according to their principal stress direction and each category is assigned with a uniform micro material. The interpolation scheme for macro elements is based on Discrete Material Optimization (DMO), where each element is assigned with m macro design variables. The categorization process of the macro structure is achieved by proper modification of volume constraints, where the macro design variables are multiplied by penalty functions. The penalty functions make it uneconomical for the usage of micro materials, which do not correspond to the principal stress direction of their macro element. The macro structure and micro material are connected through effective property, which is calculated through novel numerical implementation of asymptotic homogenization method (NIAH). Both macro structure and micro materials are optimized concurrently and analytical sensitivities are calculated with adjoint method. One minimum compliance numerical example of an L-bracket subject to volume constraints, where one micro material correspond to macro domain with principal stress angle near 0 or 90 degrees and another correspond to that with principal stress angle near 45 or 135 degrees, is presented to show the potential of the proposed method.

The superior stiffness-to-weight and strength-to-weight mechanical advantages of shell-infill structures can be fully exploited through concurrent design of the entire topology and infill configuration. This inherent design f... | Find, read and cite all the research you need on Tech Science Press

This paper proposes a concurrent multiscale optimization method of macrostructure topology and microstructure shapes for porous structures, aimed at maximizing a specified natural frequency. The multi‐material distribution of the macrostructure and the shape of the microstructures are optimized by topology and shape optimization, respectively. The homogenized properties of the porous materials are calculated using the homogenization method, and the homogenized elastic tensor and density are applied to the macrostructure. The optimum distribution of the porous material in the macrostructure is determined by a multi‐material topology optimization using the generalized solid isotropic material with penalization (GSIMP) method, which is a method to obtain multi‐material topology by implementing the successive binarization. The KS (Kreisselmeier–Steinhauser) function is introduced to solve the repeated natural frequencies issue that lies in the maximization of a specified natural frequency. An area‐constrained multiscale optimization problem is formulated as a distributed‐parameter optimization problem, and the sensitivity functions are derived using the Lagrange multiplier method and the adjoint variable method. Based on the obtained sensitivity functions, the design variables are updated using the H1 gradient method (i.e., a nonparametric shape/topology optimization method). The effectiveness of the proposed method for maximizing a specified natural frequency is confirmed through 2D and 3D numerical examples, in which the influences of sub‐regions of the macrostructure and anisotropic material of the microstructures are also investigated and the results are discussed.